I've over complicated it with background. I just want to edit one side (or face) of a cube (or a proxy side of that cube) and Blender to automatically edit all of it's sides in the same way, with a mirror modifier applied to each side, mirroring on each individual side's normal orientations of those sides, with a subdivision surface modifier applied to the whole object, on top of that. However, something that does the same job is good too, as long as it allows for real time previews of the outcome.
This is what I'm looking for:
The mirror modifier applies to only one side of the currently unmade cube. [![enter image description here]]
The mirror modifier is applied and copies of that side are joined together to form the cube.[![enter image description here]]
The subdivision surface modifier is applied to the completed cube after doubles are removed. (Not enough reputation, of which 10 is required, to post more than two links, such as images. Sorry.)
The thing is, though, that whole process is automated and happens within a tenth of a second after the base mesh (the original side) is edited and is repeated as it continues to be edited (with the necessary cleanup of objects, etc.).
Maybe programming for task automation is the solution, but I would have thought Blender would have a way of doing this without programming. (I came to Blender from Python programming, so it's no big deal to me if it requires Python programming).